Louis van Gaal's men stunned the reigning world champions as they took them apart in their opening match of the World Cup on Friday.
Two goals each from Robin van Persie and Arjen Robben, plus a Stefan de Vrij header, gave Netherlands a resounding Group B win in Salvador, despite Xabi Alonso initially putting the Spaniards ahead.
However, De Jong has demanded that his team-mates do not get carried away, reminding them that it will all count for nothing if they fail to live up to expectations against Chile and Australia, the latter of whom they play on Wednesday.
"I understand that the euphoria is very large after the 5-1 against Spain," said the AC Milan man. " But we have to give everything against Australia. Today [Sunday] was actually a recovery training session because the 48 hours after a game is often the hardest.
"In the first five minutes of the second half we started well. In the back we were compact, we won the duels and everyone worked hard. We looked at each other and were like [sic], this is going to happen today.
"Of course it was a fantastic victory. But it is only a group match. We have achieved nothing yet. As of yesterday, we are going to focus on the game against Australia."
Australia put in a decent performance in their opener against Chile, but they ultimately slumped to a 3-1 defeat.
Tim Cahill bagged the Socceroos' only goal and De Jong says the Netherlands will be looking to keep him in check.
"I have often played against him in England," he added. "He is a player who plays with his heart. He is a good header [of the ball], and often gets into the right places from crosses.
"Of course we should keep a close eye on him."
Meanwhile, left-back Daley Blind - who contributed two assists against Spain - missed some of the team’s training session on Sunday with a knee injury, but he allayed any fears about whether he will be fit to feature on Wednesday.
"As a precaution I stayed inside. I had slight problems with my knee. I don't expect any problems for the match against Australia," he said.